# What is the length of the hypotenuse of a right triangle?

## What is the length of the hypotenuse of a right triangle?

In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

### What is the hypotenuse of 6 and 8?

For example a right triangle with legs of length 6 and 8 will have a hypotenuse of 10 (62 + 82 = 102, 36 + 64 = 100).

#### What is the length of the hypotenuse of the triangle 26?

26 feet
Explanation: By Pythagoras Theorem, a2+b2=c2 . Since the hypotenuse, c is 26 feet long, 262 = 676.

What is the length of the hypotenuse of the triangle 7cm and 3cm?

So, length of hypotenuse is 7.62 cm.

How do you work out the length of the hypotenuse?

If you are given the length of the shortest leg (opposite the 30-degree angle,) simply multiply the leg length by 2 to find the length of the hypotenuse. For instance, if the length of the shortest leg is 4, you know that the hypotenuse length must be 8.

## What is the equation for 30 60 90 Triangle?

30-60-90 Triangle Rule

Base is given Perpendicular is given
The perpendicular of the triangle ABC is AB = (a /√3) The hypotenuse of the triangle ABC is AC = (2a)/√3 The base of the triangle DEF is EF = √3a. The hypotenuse of the triangle DEF is DF = 2a.

### How to calculate the hypotenuse of a right triangle?

Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²) Given angle and one leg. c = a / sin(α) = b / sin(β), from the law of sines. Given area and one leg.

#### Which is the sum of the two sides of the hypotenuse?

The Pythagorean Theorem states: In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

How did Pythagoras come up with the hypotenuse theorem?

The Pythagorean Theorem is a well-known theorem developed by a Greek mathematician named Pythagoras around 500 BC. It related the length of the hypotenuse of a right triangle to the lengths of the legs (the legs of the triangle are the two shorter sides).

How to calculate the sides of the right triangle?

b = √ (c² – a²) for hypotenuse c missing, the formula is. c = √ (a² + b²) Given angle and hypotenuse. Apply the law of sines or trigonometry to find the right triangle side lengths: a = c * sin (α) or a = c * cos (β) b = c * sin (β) or b = c * cos (α) Given angle and one leg.